airy (MATLAB Functions)

Airy functions

Syntax

W = airy(Z)
W = airy(k,Z)
[W,ierr] = airy(k,Z)

Definition

The Airy functions form a pair of linearly independent solutions to

The relationship between the Airy and modified Bessel functions is

where

Description

W = airy(Z) returns the Airy function, , for each element of the complex array Z.

W = airy(k,Z) returns different results depending on the value of k.

k
Returns

0
The same result as airy(Z)

1
The derivative,

2
The Airy function of the second kind,

3
The derivative,

k	Returns
`0`	The same result as `airy(Z)`
`1`	The derivative,
`2`	The Airy function of the second kind,
`3`	The derivative,

[W,ierr] = airy(k,Z) also returns completion flags in an array the same size as W.

ierr
Description

0
airy succesfully computed the Airy function for this element.

1
Illegal arguments

2
Overflow. Returns Inf

3
Some loss of accuracy in argument reduction

4
Unacceptable loss of accuracy, Z too large

5
No convergence. Returns NaN

ierr	Description
`0`	`airy` succesfully computed the Airy function for this element.
`1`	Illegal arguments
`2`	Overflow. Returns `Inf`
`3`	Some loss of accuracy in argument reduction
`4`	Unacceptable loss of accuracy, `Z` too large
`5`	No convergence. Returns `NaN`

See Also

besseli, besselj, besselk, bessely

References

[1] Amos, D. E., "A Subroutine Package for Bessel Functions of a Complex Argument and Nonnegative Order," Sandia National Laboratory Report, SAND85-1018, May, 1985.

[2] Amos, D. E., "A Portable Package for Bessel Functions of a Complex Argument and Nonnegative Order," Trans. Math. Software, 1986.

addproperty (COM) alim